Annals of Operations Research

, Volume 264, Issue 1–2, pp 41–56 | Cite as

Efficient extensions of communication values

  • Sylvain Béal
  • André Casajus
  • Frank Huettner
Original Paper


We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some deletion link property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (Soc Choice Welf 45:819–827, 2015) prove that the Myerson value (Myerson in Math Oper Res 2:225–229, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (Econ Lett 117:786–789, 2012). We pursue this line of research by showing that the average tree solution (Herings et al. in Games Econ Behav 62:77–92, 2008) and the compensation solution (Béal et al. in Int J Game Theory 41:157–178, 2012b) admit similar unique efficient extensions, and that there exists no efficient extension of the position value (Meessen in Communication games, 1988; Borm et al. in SIAM J Discrete Math 5:305–320, 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions.


Efficient extension Average tree solution Compensation solution Position value Component fairness Relative fairness Balanced link contributions Myerson value Component-wise egalitarian solution 

Mathematics Subject Classification


JEL Classification



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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.CRESE EA3190Univ. Bourgogne Franche-ComtéBesançonFrance
  2. 2.HHL Leipzig Graduate School of ManagementLeipzigGermany
  3. 3.ESMT European School of Management and TechnologyBerlinGermany

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